Methods

National aquatic resource survey data for the 2007 National Lake Assessment (NLA) was retrieved from USEPA. Water quality parameters including dissolved organic carbon, total phosphorus, total nitrogen and silica (SiO₂) were used to evaluate stoichiometric relationships across the nine wadable stream assessment ecoregion (Fig 1; Herlihy et al., 2008). Values reported as zero were excluded from analysis, values reported less than the minimum detection limit were set to the historic average minimum detection limit (USEPA, 2009).

Figure 1. Ecoregions used in the National Aquatic Resource Surveys link

Prior to analysis surface water nutrient concentrations were converted from mass of nutrient per volume concentration (i.e. mg L^-1) to molar concentrations (i.e. mM). Nutrient stoichiometric relationships within each ecoregion were examined by evaluating power law slopes using standardized major axis (SMA) regression (’smatr’ package; Warton et al. 2006) consistent with Cleveland and Liptzin (2007). Unlike standard regression techniques which are used to predict one variable from another, SMA regression assesses the best fit line between two variables. Molar nutrient concentrations were log-transformed and slope of the SMA regression was evaluated against the null hypothesis that the slope was not different from one (\(\beta \neq1\)). Power law (\(y=kx^{\beta}\)) and its linearized form (\(log(y) = \beta log(x) + log(k)\)) are used to evaluate the degree of proportional scaling between two variables. Scaling relationships and power-law distributions are key to understanding fundamental ecological relationships and processes in the natural system such as energy acquisition and transformation, biomass-growth relationships and evaluation of watershed chemostasis (Brown et al., 2002; Marquet et al., 2005; Wymore et al., 2017). In this analysis, we tested if the slope of the SMA regression results were statistically significantly different from one (i.e. \(\rho\) < 0.05) and interpreted as the variables are independent and do not proportionally scale (i.e. allometric growth) where one nutrient can either be enriched or depleted relative to the other (Fig 2). If the slope was not statistically different from one (i.e. \(\rho\) > 0.05), then the variables exhibited proportional changes (i.e. isometric growth; Fig 2) resulting in a constrained stoichiometry between nutrients. A slope not different from one would indicate that for any given concentration of nutrient X (i.e. C, N, or P) a proportional concentration of nutrient Y (i.e. P, C or N) existed. The degree of scaling (i.e. slope test) was combined with an evaluation of the regression coefficient of determination (R²) which indicated the degree of predictability (i.e. one nutrient can be used to predict the other). Low R² values reflected high stoichiometric variability suggesting a decoupling of nutrients while high R² values reflected low stoichiometric variability indicating a degree of coupling between nutrients. For our purposes, decoupled stoichiometric relationships were defined as a relationship with an R² less than 0.25, R² greater than 0.25 suggested some degree of coupling.

All statistical operations were performed with R (Ver 3.1.2, R Foundation for Statistical Computing, Vienna Austria), unless otherwise stated all statistical operations were performed using the base R library. The critical level of significance was set at \(\alpha\) = 0.05. Unless otherwise stated, mean values were reported with together with standard errors (i.e. mean \(\pm\) standard error).

Figure 2. Conceptual model for power law slope (β<U+F062>) interpretation relative to log transformed nutrient concentrations and relationship to stoichiometric ratios (i.e. X:Y)